Ampere's Law derivation and explanation applied physics .pptx

A presentation that explains the concept of amperes law and shows the complete derivation along with real life usage.

1. Amperes law Group #2:- Muhammad Rehan Azhar Zaid Younes Muhammad Rehan Muhammad Haris Tanvir Muhammad Usman

2. Table of contents 02 Case 1:Field outside the wire loop 01 Definition & Derivation 04 Numerical 03 Case 2: Field inside the wire loop

3. “ Ampere’s law states that for any closed path (Amperian loop), the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop .” — André-Marie Ampère

4. Origin: Ampere's law was formulated by André-Marie Ampère in the early 19th century as a mathematical expression of the magnetic field produced by a current-carrying conductor. Integral Formulation: The law states that the magnetic field ( B ) around a closed loop is directly proportional to the current ( I ) passing through the loop and inversely proportional to the distance ( r ) from the current. It is mathematically expressed as ∮ B ⋅ d l = μ 0​⋅ I enc ​ , where μ 0​ is the permeability of free space and I enc ​ is the enclosed current. Symmetry: One of the powerful aspects of Ampere's law is its symmetry, especially for symmetric current distributions. It allows for the calculation of magnetic fields for highly symmetrical situations, such as straight wires, solenoids, and toroid. Applications: Ampere's law finds widespread applications in various fields, including electrical engineering, physics, and technology. It helps in designing electromagnets, understanding magnetic field configurations around conductors, and even in the development of devices like MRI machines. Limitations: Ampere's law is valid only under specific conditions, primarily when the current is steady and the magnetic field is constant in time. It does not hold true for situations involving changing electric fields or time-varying magnetic fields, where Maxwell's equations are necessary

5. Derivation of Amperes law

6. Case 01 Magnetic Field Outside a Long Straight Wire with Current

7. Ampere's Circuital Law: This principle states that the magnetic field ( B ) around a long straight wire is directly proportional to the current ( I ) passing through the wire. It's inversely proportional to the distance ( r ) from the wire. Right-Hand Rule: Applying the right-hand rule helps determine the direction of the magnetic field. If the thumb of the right hand points in the direction of current flow, the curled fingers represent the circular magnetic field lines around the wire. Field Strength Formula: The formula to calculate the magnetic field strength ( B ) at a distance r from the wire is B = μ 0​⋅ I / ​2 πr , where μ 0​ is the permeability of free space ( 4 π ×10−7Tm/A ). Field Distribution: The magnetic field strength decreases with increasing distance from the wire. It follows an inverse relationship ( 1/ r ) with distance, depicting the field's rapid decrease with distance. Field Lines Configuration: The magnetic field lines form concentric circles around the wire, creating circular patterns perpendicular to the wire's axis. These lines indicate the direction and strength of the magnetic field at various distances from the wire.

8. Magnetic field outside the wire

9. Case 02 Magnetic Field inside a Long Straight Wire with Current

10. Symmetrical Field Distribution: Due to the uniform distribution of current in a long straight wire, the magnetic field it produces is cylindrically symmetrical around the wire. Amperian Loop for Analysis: To determine the magnetic field within the wire, an Amperian loop of radius r (where r < R ) is used. This loop helps in calculating the magnetic field strength at different distances from the wire. Ampere's Law Application: Ampere's Law, applied using the Amperian loop, shows that the magnetic field's magnitude ( B ) inside the wire ( r < R ) is directly proportional to the radial distance ( r ) from the wire. Variation of Magnetic Field: Inside the wire, the magnetic field strength ( B ) is zero at the centre ( r =0 ) and increases linearly with the radial distance, reaching its maximum at r = R (the surface of the wire). Proportional Relationship: The magnitude of the magnetic field ( B ) is directly proportional to the radial distance ( r ) from the wire's axis within the wire's confines. Comparative Analysis: The equations demonstrate that the magnetic field's value at the wire's surface ( r = R ) is the same, both from the outside ( r = R ) and inside ( r = R ) perspectives.

11. Numerical related to topic

12. The Endless End